Keynes

1
Keynes Beauty Contest Speculative Price
Bubbles in the Absence of Common Knowledge in
Experimental Stock Markets

• Shinichi Hirota and Shyam Sunder
• University of Iowa Workshop, Dec 7, 2001

2
Valuation of Securities

• Value net present value of future cash flows
• Future is uncertain, value depends on investor
  beliefs about the future cash flows
• How far into the future?
• From now to liquidation of the the security
• From now to investment horizon (sale)
• Sale price depends on beliefs of other investors
  about the cash flows after the sale
• Return to formalization later

3
Simple Example

• Investor A believes the net present value of cash
  flows from now on to be 100 (fundamental value)
• Investor should buy below 100 and sell above
• What if A also believes that tomorrow, others
  will believe the net present value to be 150
• Considering second order beliefs, it may not
  necessarily be best for A to sell at 110. A may
  be better off buying at that price, with the
  expectation of being able to sell at a higher
  price
• What is the best thing to do for an investor
  whose first and second order beliefs are not
  identical?

4
Stories of Common Knowledge Assumption

• In a great deal of business modeling, common
  knowledge is routinely assumed
• What happens when it breaks down?

5
Emperor Has No Clothes
6
(No Transcript)
7
Emperors Clothes

• The scoundrels made people believe that the
  clothes will be invisible only to the incompetent
  and the stupid
• People thought that others believed it
• Nobody wants to be seen as stupid or incompetent
  by others, lose his/her job
• Visibility of clothes was private, it was easy to
  fake seeing the clothes

8
Emperors Clothes (Contd.)

• Scenario 1 Everyone was privately convinced of
  their incompetence, and cheered to deny it
  publicly
• Scenario 2 People did not believe they were
  incompetent just because they could see the naked
  emperor, but believed that others so believed,
  and cheered to avoid being seen as stupid

9
What about the Child?

• The child did not know the link between
  visibility and competence
• Child was innocent, and said what he saw
• People know children to be innocent
• People knew that people knew this

10
Stock Market

• Stock Market is like a newspaper beauty contest
• John Maynard Keynes, (1936)

11
Newspaper Beauty Contest
Which Face is the prettiest?
12
Which face will they judge to be the prettiest?
13
Which face will they judge to be the prettiest?
14
LIFO Inventory Accounting

• If your inventory prices rise, and end-of-year
  inventory volume is stable or rising
• You can delay paying taxes (higher net present
  value of cash flows)
• But have to report lower income also
• Many firms dont adopt LIFO
• Apprehension about stock market reaction (no
  empirical support)

15
Agency Problem

• Agency problem how to induce managers to
  maximize shareholder value (e.g., choose LIFO)
• Solution Link managerial compensation to
  shareholder value
• Problem 2 Value manipulation
• Solution Use market, not accounting, measures of
  value

16
Value Maximizing Manager in an Efficient Market

• LIFO can increase NPV of cash flow
• But manager maximizes stock price
• What does manager believe about how stock prices
  are determined?
• Suppose manager believes that stock prices depend
  on income, not cash
• Then manager is rationally led to reject LIFO
  even if it saves cash for the firm

17
Beliefs About Others Beliefs

• Common elements to the three stories about the
  emperors clothes, stock market and LIFO
• Central role of what we believe about others, and
  about their beliefs

18
Closing the Gap in Beliefs

• Is it possible for our first and higher order
  beliefs to differ?
• When they do differ, what does it take to get
  them to converge? Aumann (1976).
• Do they actually converge? Why or why not?
• When the beliefs of all around you are wrong,
  does it pay to hold on to the right beliefs?
  Fight them or join them?
• Prior experimental results
• What are the consequences for theories of bubbles?

19
Bubbles in Economic History

• Self-evident bubbles Galbraith, Kindleberger
• Econometric studies of long term recorded data
  stock prices move sufficiently closely with
  dividend over the long run to reject bubbles
• Contemporary investors knew more than what the
  econometricians have in their data
• What changes in fundamentals can justify the 90
  percent price drop during the Great Crash?

20
Beliefs and Observation

• Theories of valuation are a function of beliefs
• In the field it is difficult enough to know the
  first order investor beliefs, and their diversity
• Second and higher order beliefs are practically
  out of reach
• In lab we might have a better, though still
  limited, chance to know beliefs, perhaps even
  open a gap between the first and higher order
  beliefs and observe their consequences under
  controlled conditions

21
Models of Bubbles

• Tirole (1082, 1985) bubbles grow at discount
  rate, no prediction about levels
• First order beliefs Dti ? Dtij (second order
  beliefs)
• Investor need not be irrational in decisions or
  beliefs, and need not believe the others to be
  irrational.
• Aumann common knowledge priors imply common
  knowledge posteriors

22
Professional Security Analysis

• Multi-billion dollar information intermediary
  industry in U.S. alone
• Typical report has current market price compared
  to what the analyst predicts the future price to
  be, and what the analyst believes the firm to be
  worth
• If investor beliefs were common knowledge, there
  will be no rationale for such beliefs
• Bubbles generated by gap between the first and
  second order beliefs do not depend on investor
  heterogeneity

23
Finite Maturity Securities
24
Finite Maturity Securities

• Cells C and D (sessions 3 and 4)
• All dividends except terminal dividends are zero
• Equilibrium price is constant through the 15
  sessions
• By design, second order beliefs have the chance
  of being higher than the first order beliefs
• Expect to observe bubbles as late as period T-1
  in Cell C
• Expect the bubble to crash in the last period
  (Figure B)

25
Indefinite Maturity Securities
26
Indefinite Maturity Securities

• Cells A and B
• All dividend except liquidation dividend are zero
• Session does, and is expected to end before
  liquidation
• Terminal payoff by endogenous prediction game
  (see Figure A for price path)

27
Experimental Design

• Double auction market for multiple units of a
  single security that pays single liquidating
  dividend
• Multiple trading periods (3 minutes each)
• Each investor endowed with 10 shares, 10,000
  points in cash
• Liquidation by dividend or predicted price
• Predictors knew the rules, no endowments, no
  ability to trade, could watch trading, knew the
  range of terminal dividends

28
Experimental Design

29
Experimental Parameters
30
Trading Screen
31
(No Transcript)
32
Cell A (Session 1)

• Endogenous, gap
• Small bubble (10 percent)
• Highly stable
• No crash
• High correspondence between actual and predicted
  prices
• Efficient security transfer late but not early

33
(No Transcript)
34
Cell B (Session 2)

• Endogenous, no gap
• Huge bubble, well above second order belief
  limits
• Highly stable
• Did not crash
• Allocations suggest that terminal dividends
  ceased to play any important role in driving
  trading, largely driven by prediction

35
Tentative Conjectures

• Conjecture 1 In absence of exogenously specified
  terminal dividend, price bubbles can form, and
  persist through the end of a session.

36
(No Transcript)
37
Cell C (Session 3)

• Exegenous termination, gap
• Large bubble, prices above upper limit of second
  order beliefs
• Bubble burst earlier than last period
• Error by one trader (forgot terminal dividend)

38
(No Transcript)
39
Cell D (session 4)

• Exogenous termination, no gap
• No bubble
• Fundamental price and allocations

40
Tentative Conjectures

• Conjecture 2 Even with exogenous terminal
  dividend and known horizon, bubbles can form when
  there is a gap between first and second order
  beliefs.
• Conjecture 3 In the presence of exogenously
  specified terminal dividend, end-of-the-session
  prices converge to the equilibrium level
  determined by such dividends.

41
(No Transcript)
42
Results A Gap, Endogenous Termination
43
Discussion

• Shiller prices too volatile
• French and Roll Market trading itself creates
  volatility (possibly through formation of second
  order beliefs?)
• Significant part of market returns realized as
  capital gains, not dividends
• Valuation models should incorporate second order
  beliefs

44
Discussion

• Stock prices can stabilize far from fundamental
  price levels
• Price predictions can simply reinforce deviations
  from fundamentals
• In a market dominated by capital gains traders,
  price can be decoupled from fundamentals
• Consistent with gap between first and higher
  order beliefs generating price bubbles

45
Bubbles and Rationality

• Lei, Noussair and Plott observe bubbles in
  absence of speculative trading
• Lack of understanding by subjects of the market
  structure, task, opportunities
• Lack of correspondence between the intended and
  subjective experimental environment
• Difficult to determine the correspondence
• Is lack of understanding irrational?
• Need get inside irrationality.

46
Candidates to be Examines

• Gap between intended and subjective experimental
  environment
• We tried this in a fifth session observed many
  errors in spite of better instructions
• Link between uncertainty and bubbles
• Link between low dividend securities (larger
  duration) and bubbles

47
Thank You

• The paper will be available on
• http//www.som.yale.edu/faculty/sunder/research
• My email is shyam.sunder_at_yale.edu

48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
Financial Analysis, Trading Volume and Bubbles

• Mostly fundamental analysis, assumes common
  knowledge
• Assumption relaxed by convenience
• Models of price bubbles based on relaxing the
  common knowledge assumption
• Trading volume models based on diverse beliefs

52
Models of Weakening Common Knowledge Assumption

• Efficient markets may fail to discipline managers
  (Amershi and Sunder)
• Alternatives to fundamental valuation model, even
  technical models
• Models of corporate disclosure (unraveling does
  not work in practice)
• Understanding results of ultimatum games

53
(No Transcript)
54
Levels of Analysis
55
Thank You

• The paper, and slides will be available next week
  at
• http//www.som.yale.edu/faculty/sunder/research.ht
  ml
• or email to shyam.sunder_at_yale.edu

56
The purpose of our study

• Explore why the price bubble occurs in stock
  markets
• Investors belief on others belief
• Stock market experiments

57
Stock market bubble in the real world

• Internet Bubble
• e.g. Yahoo
• 10 now, 250 in the peak
• Japan late 80s
• e.g. Nikkei 225 Average
• 10,000 yen now, 40, 000 yen in the
  peak
• Must be bubbles
• Why bubbles occur

58
Investor should expect ...

• Infinitely lived investor
• Discounted value of future dividends
• Finite horizon investor
• Resale price
• Others valuation
• Others expectation for the future
• Future dividends
• Future price

59
If he believes that

• Others will believe high future dividends or high
  future price,
• What should he do?
• Even if he does not believe high future dividends
  or high future price.

60
If every investor believes that

• Others will believe high future dividends or high
  future price,
• What will happen?
• Even if every investor himself does not believe
  high future dividends or high future price

61
Stock prices

• are determined by
• not investors own beliefs
  (first-order-beliefs)
• but investors beliefs on others beliefs
  (second-order-beliefs)
• Any Price can be observed depending on
  second-order-beliefs

62
Bubbles

• Price ? Fundamental Value
• Price
• Second-order-belief
• Fundamental Value
• First-order-belief
• Second-order-belief ? First-order-belief

63
Keynes

• Newspaper beauty contests
• Well-known and popular story
• True in real world?
• How to verify?
• Fundamental value is unobservable
• Gap is unobservable

64
Experimental Study

• Laboratory
• Fundamental value is observable
• Create the gap between FOB and SOB
• See the effect of the gap on the stock price
• Experimental Results
• Bubbles occurred due to the gap
• Keynes is right!

65
Experimental Markets

• Stock market in the laboratory
• Trade a single stock
• 15 (12) periods of 3 minutes each
• Stocks has a life during the experiment

66
How to create the gap between FOB and SOB

• Each investor knows dividends (FOB)
• But SOB may be different from FOB
• Market 1
• Dividends may not be received in the investment
  life.
• Dividends are paid only if the session lasts for
  30 periods
• The subjects can easily guess that the session
  ends earlier
• The stock at the last period is evaluated at the
  predicted price of the next period
• They have to expect what the market expects the
  price

67
How to create the gap between FOB and
SOB(continued)

• Market 2
• 15 periods. Dividends are paid at the end of
  Period 15.
• Each knows his dividend, but does not know
  others dividends
• Investors draws the dividend card
• Private information
• The dividend range is informed to everyone
• Investors have to guess others dividends, i.e.,
  others valuation of the stock.

68
Investrors and Predictors

• Investors
• 10 stocks, 10,000 cash
• trade stocks using caplabTM system
• receive money depending on profits
• Predictors
• predict the next periods price
• receive money depending on the accuracy

69
Conducted Experimentswhat, who, where, when

• 2 sessions for Market 1 (Session 1, 2)
• 1 session for Market 2 (Session 3)
• Yale university, undergraduate students
• Yale School of Management, B-74 Room
• September 21, 29, 30, 2001

70
Conclusion (from preliminary experimental
results)

• The investors beliefs on others belief (SOB)
  significantly affect the stock prices.
• The gap between FOB and SOB seems to create
  bubbles in stock markets.